Hawkes过程的竞争风险解释
A competing risks interpretation of Hawkes processes
摘要：
我们给出了Hawkes过程作为一个分段竞争风险模型的构造。我们认为，最自然的解释自激内核是一个有缺陷的随机变量的风险函数。这建立了所需的定性特征的过程和参数形式的内核之间的联系，我们说明使用的例子从文献中。两个家庭的治愈率模型取自生存分析文献中提出的自激核的新模型。最后，我们表明，竞争风险的观点，导致一个通用的模拟算法，避免反转补偿点过程或执行一个接受拒绝的步骤，因此是快速和相当普遍的。
英文摘要：
We give a construction of the Hawkes process as a piecewise competing risks model. We argue that the most natural interpretation of the self-excitation kernel is the hazard function of a defective random variable. This establishes a link between desired qualitative features of the process and a parametric form for the kernel, which we illustrate using examples from the literature. Two families of cure rate models taken from the survival analysis literature are proposed as new models for the self-excitation kernel. Finally, we show that the competing risks viewpoint leads to a general simulation algorithm which avoids inverting the compensator of the point process or performing an accept-reject step, and is therefore fast and quite general.
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